The Maccabees should be celebrating. When we meet, on the threshold of their biggest tour to date, the south London five-piece have just heard that they're at No 1 in the midweek chart, while they are currently gracing the cover of the NME, hailed "the best guitar band in Britain". Not that they are in mid-celebration.

"Midweek," stresses their overly cautious singer and lyricist Orlando Weeks. "This is the thing... it can all change very dramatically." Somewhat more encouraged is the five-piece's guitarist, Felix White. "Just the fact that is it is even for a second is..." he pauses, lost for words. "I hadn't even entertained the thought that it would be, so that's amazing. I'm ready to celebrate that, even if it ends up at 25."

It did drop a few places, but only to No 4, landing them their first Top 5 album, at a time when guitar music is supposedly in trouble and out of favour. The success led them to announce a date, this June, at Alexandra Palace, the 10,000-capacity venue where bands including Arcade Fire, Sigur Ros and Interpol before them – and now The Black Keys – have cemented their status. It's clear that The Maccabees' time is now.

Perhaps their reluctance to shout about it is to do with the fact that their success has been a long time in the making. Since the close-knit group of friends, including White's younger brother Hugo on guitar and Rupert Jarvis on bass (drummer Sam Doyle joined after the debut album), formed in 2004 as a more productive alternative to spending the whole of the summer sitting on Clapham Common doing "absolutely nothing" ("we had to start doing something, just to spend time doing more productively and then also to maintain that togetherness," recalls Weeks), The Maccabees have been quietly toiling away on the guitar-band circuit. They have slowly built success, from their single "Toothpaste Kisses", which found its home on a Samsung advert, to the higher chart placing (No 13) of their second album Wall of Arms in 2009, which led to sell-out performances at Brixton Academy.

"The way it's gone for us is that we have just slowly, slowly crept up the table," says Weeks. "Each album we've got to play bigger places as a statement, almost, although it doesn't feel like that's what it is to us. [The Alexandra Palace gig] is a really nice thing to look forward to and work towards.."

They don't regret the slow ascent; they wouldn't have had it any other way. "It's definitely very positive for us," says White. "If the first record had happened to be a big record, it would have been difficult to keep us all together because we weren't sure what we were doing. We're still not, now, but you need to have space in order to work it out. I'm glad it's happened how it's happened. We still don't feel like a big band."

The new album, Given to the Wild, is their most ambitious to date, leaving behind the angular indie of their beginnings to take on a thoughtful and dreamy mood, drawing in cyclical riffs, subtle layers of guitar, and even prog-rock. They put their sound development down to their new method of songwriting. While both their debut and sophomore albums were created as a collective with the skeleton of Weeks's songs as a starting point, for Given to the Wild there was a democratic decision to each go their own ways, to their respective south London homes, to work on their ideas.

"Up to that point we'd only written in rented rehearsal rooms that you have for a day," explains White. "By the time we'd finished our second record it just felt limiting and we were bored of that process, so it made sense, with people having bigger ideas." It was a way of allowing all the band members a part in the songwriting process, "keeping everyone happy and it still being The Maccabees and it not falling apart... In the writing it feels there's an easiness," adds Weeks. "The change – and taking some of that pressure away from the claustrophobic room environment – I think that definitely made a huge difference."

White cites The Colour of Spring and Spirit of Eden by Talk Talk "and the space in it" as inspiration. Weeks had found himself drawn to expansive songs such as The Cars' "Drive" and Bruce Springsteen's "Streets of Philadelphia". "I was listening to these shamelessly enormous songs and trying to understand how that works, how the vocal melody could be that slow or that repetitive. I thought there must be a secret to these vocal lines."

With the space afforded them – the album was written over a luxuriously paced two years – lyricist Weeks had plenty of time to ponder the themes for the album, which include growing up and mortality.

"Going from being really busy to having this free time gives you a lot more time to think about stuff that there really isn't any point thinking about," says Weeks, at 28 the oldest of a band which ranges from 25. "Everyone being of an age where people that you've grown up with are suddenly starting to become parents and becoming serious members of society, it felt like something worth cataloguing."

Final work on the album – and all their rehearsing – took place in the studio where we meet, in Elephant and Castle, London. While Call to Arms was stamped with the sound of Arcade Fire due to the production work of Markus Dravs, by album three they had honed their recording skills to the point of being more reliant on themselves. It's how they were able to create their distinctive sound on Given to the Wild.

"In a production sense we had a lot more understanding of how we wanted it to be," says White. "Whereas in the first two we put it in their [the producers'] hands, with this one, from the very start, we could mould it into how it sounds now." While in the past they felt they had more of a sense of identity live than on record, this album saw them take more risks musically. Weeks explains: "This time we made a record to sound like a record, we didn't put those limitations on ourselves."

The other side to creating more complex songs is, of course, that they are harder to replicate live. "There's too much going on in this record to do it all live without faking loads of stuff, which we don't want to do," says White. "One of the first proper support tours we did was with Jamie T and the Pacemakers and Jamie had made an amazing bedroom record and when the Pacemakers were playing it would be totally different, but it would be fine. No one wanted to see the exact same version, so we've learned something from that this time round. It's tempting to literally recreate it."

Weeks adds: "Often it's better to slightly sacrifice in terms of the layers of things going on. You compensate for that with performance – and loudness." Now that they are feeling confident, they have been reading reviews of their album, something which they'd avoided for fear of being knocked back.

"I was worried I'd be hurt reading negative things," admits White. "But this time we feel good about the record and assured enough to be able to take it on the chin." Weeks adds: "I read that the record sounded like a witch-house version of the Lion King soundtrack, which sounds amazing," says Weeks. "But I don't think it was intended to be a compliment." The news that they ended up higher in the chart than Beyoncé that week came as welcome relief. "I got a phone call from my landlord saying that my rent had bounced," says White. "That sums it up, really."